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From: Ian Kelly <ian.g.kelly@gmail.com>
Date: Thu, 19 Feb 2015 11:32:17 -0700
Subject: Re: python implementation of a new integer encoding algorithm.
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On Thu, Feb 19, 2015 at 11:24 AM, Dave Angel <davea@davea.name> wrote:
> Here's a couple of ranges of output, showing that the 7bit scheme does
> better for values between 384 and 16379.
>
> 382 2 80fe --- 2 7e82
> 383 2 80ff --- 2 7f82
> 384 3 810000 --- 2 0083
> 384  jan grew 3 810000
> 385 3 810001 --- 2 0183
> 386 3 810002 --- 2 0283
> 387 3 810003 --- 2 0383
> 388 3 810004 --- 2 0483
> 389 3 810005 --- 2 0583
>
> 16380 3 813e7c --- 2 7cff
> 16380  jan grew 3 813e7c
> 16380 7bit grew 2 7cff
> 16381 3 813e7d --- 2 7dff
> 16382 3 813e7e --- 2 7eff
> 16383 3 813e7f --- 2 7fff
> 16384 3 813e80 --- 3 000081
> 16384 7bit grew 3 000081
> 16385 3 813e81 --- 3 010081
> 16386 3 813e82 --- 3 020081
> 16387 3 813e83 --- 3 030081
> 16388 3 813e84 --- 3 040081
> 16389 3 813e85 --- 3 050081
>
> In all my experimenting, I haven't found any values where the 7bit scheme
> does worse.  It seems likely that for extremely large integers, it will, but
> if those are to be the intended distribution, the 7bit scheme could be
> replaced by something else, like just encoding a length at the beginning,
> and using raw bytes after that.

It looks like you're counting whole bytes, not bits. That would be
important since the "difficult" encoding uses fractional bytes.